The Quantum Transition of the Two-Dimensional Ising Spin Glass: A Tale of Two Gaps

Abstract

Quantum annealers are commercial devices aiming to solve very hard computational problems named spin glasses. Just like in metallurgic annealing one slowly cools a ferrous metal, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. The field removal diminishes quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, as compared to classical computers, rest on the assumption that the gap will close algebraically with the number of qspins, but renormalization group calculations predict that the closing will be instead exponential. Here we solve this debate through extreme-scale numerical simulations, finding that both parties grasped parts of the truth. While the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. Since this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the Quantum Annealing paradigm.

References in corpus (7)

• Quantum critical dynamics in a 5000-qubit programmable spin glass
• The critical behavior of three-dimensional Ising spin glass models
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Critical and Griffiths-McCoy singularities in quantum Ising spin-glasses on d-dimensional hypercubic lattices: A series expansion study
• The QISG suite: high-performance codes for studying Quantum Ising Spin Glasses

Cited by in corpus (19)

• Beyond-classical computation in quantum simulation
• Scaling Advantage in Approximate Optimization with Quantum Annealing
• Pushing the Boundary of Quantum Advantage in Hard Combinatorial Optimization with Probabilistic Computers
• Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
• Spin-glass dynamics: experiment, theory and simulation
• Limitations of tensor network approaches for optimization and sampling: A comparison to quantum and classical Ising machines
• Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Hyperoptimized approximate contraction of tensor networks for rugged-energy-landscape spin glasses on periodic square and cubic lattices
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Boosting quantum annealing performance through direct polynomial unconstrained binary optimization
• Wideband covariance magnetometry below the diffraction limit
• Random displacements in critical Rydberg atom arrays
• Quantum sequel of neural network training
• Graph Coloring via Quantum Optimization on a Rydberg-Qudit Atom Array
• Ancillary entangling Floquet kicks for accelerating quantum algorithms
• Energy gap of quantum spin glasses: a projection quantum Monte Carlo study
• Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
• Evidence of de Almeida-Thouless line below six dimensions